What is inverse oflaplace (20)/(s(s+30)) ?

The answer to inverse oflaplace (20)/(s(s+30)) is 2/3 \H(t)-2/3 e^{-30t}

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inverse oflaplace (20)/(s(s+30))

inverse laplace

\frac{20}{s ( s + 30 )}

\frac{2}{3} H (t) - \frac{2}{3} e^{- 30 t}

Solution steps

L^{- 1} {\frac{20}{s ( s + 30 )}}

Take the partial fraction of

\frac{20}{s ( s + 30 )} : \frac{2}{3 s} - \frac{2}{3 ( s + 30 )}

= L^{- 1} {\frac{2}{3 s} - \frac{2}{3 ( s + 30 )}}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{2}{3 s}} - L^{- 1} {\frac{2}{3 ( s + 30 )}}

L^{- 1} {\frac{2}{3 s}} : \frac{2}{3} H (t)

L^{- 1} {\frac{2}{3 ( s + 30 )}} : \frac{2}{3} e^{- 30 t}

= \frac{2}{3} H (t) - \frac{2}{3} e^{- 30 t}

\int 2 cos (t) + sec^{2} (t) d t

\frac{\partial}{\partial x} (ln ((1 - T) \cdot w \cdot x))

\frac{d y}{d x} + 2 y = 4 x

9 π^{3}

arcsin (2 x)

What is inverse oflaplace (20)/(s(s+30)) ?
The answer to inverse oflaplace (20)/(s(s+30)) is 2/3 \H(t)-2/3 e^{-30t}